Abstract: | Suppose that in a domain R(, B) of variables (r, ): (0 r , 1 +B(r–r
0
) 2–B(r–r0), where > 0, B > 0, 1 < 0 < 2 are numbers) a metric ds2 = dr2 +G(r, )d
2 and a function k(r, ) are given. The problem of isometrically immersing ds2
in E
4
with prescribed Gaussian torsion is considered. The following is proved: The class C
5
metric ds
2
is locally realized in the form of a class C
3
surface F
2
whose Gaussian torsion is the prescribed class C
3
function (r, ).Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 38–47, 1992. |